Abstract
The estimation of the standard deviation of noise contaminating an image is a fundamental step in wavelet-based noise reduction techniques. The method widely used is based on the mean absolute deviation (MAD). This model-based method assumes specific characteristics of the noise-contaminated image component. Three novel and alternative methods for estimating the noise standard deviation are proposed in this work and compared with the MAD method. Two of these methods rely on a preliminary training stage in order to extract parameters which are then used in the application stage. The sets used for training and testing, 13 and 5 images, respectively, are fully disjoint. The third method assumes specific statistical distributions for image and noise components. Results showed the prevalence of the training-based methods for the images and the range of noise levels considered.
Highlights
Noise reduction plays a fundamental role in image processing, and wavelet analysis has been demonstrated to be a powerful method for performing image noise reduction [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
Undecimated wavelet transforms have been considered for image noise reduction [3, 4, 5, 6, 10, 11, 12] as well as the decimated transforms [1, 2, 6, 7, 8, 9]
The problem of the noise standard deviation level estimation over the wavelet component is considered in this work
Summary
Noise reduction plays a fundamental role in image processing, and wavelet analysis has been demonstrated to be a powerful method for performing image noise reduction [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. Several techniques have been presented to estimate these parameters based on the median operator or on the histogram of the wavelet transform [6, 22] Other techniques, such as the minimax threshold, global universal threshold, Sure threshold, and James-Stein threshold, have been proposed in numerous works [1, 2, 7]. Experiments performed to compare the performances of these techniques [23, 24] demonstrated that it is not possible to say which is the best, even if the global universal threshold appears to be the worst These techniques assume the knowledge a priori of the noise standard deviation level; its correct estimation dramatically affects the performances of the noise reduction technique.
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